He stoked the fire in his forge higher, pulled out a dark gray, ceramic-looking beaker, and dropped her ring inside
Actually he would be pulling out what they referred to as a flask back then and it would be glowing bright red, as it is the same temperature as the forge. So you wouldn't know it was dark grey.
And the diamond would be in pretty poor shape after the high heat and the quick water quench. Classically they would clip off the prongs retaining the diamond and it would fall free.
And he wouldn't plunge the mold into a bucket of water just the solidified gold.